Question: Reliability of Testing A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80%

Reliability of Testing A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. (This 5% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive."

(a) Using Bayes' Theorem, if a person tests positive, determine the probability that the person is infected.

(b) Using Bayes' Theorem, if a person tests negative, determine the probability that the person is not infected.

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